Contact plane

Figure 16.6 illustrates the internal surface of a section removed from the center of a tube in the second pass. It is apparent from the external surface (Fig. 16.7) that the large, irregular perforation is located along the edge of the contact plane of the tube with a baffle. 

Let US now look at how this contact geometry influences friction. If you attempt to slide one of the surfaces over the other, a shear stress fj/a appears at the asperities. The shear stress is greatest where the cross-sectional area of asperities is least, that is, at or very near the contact plane. Now, the intense plastic deformation in the regions of contact presses the asperity tips together so well that there is atom-to-atom contact across the junction. The junction, therefore, can withstand a shear stress as large as k approximately, where k is the shear-yield strength of the material (Chapter 11). 

In a 3D system, however, it becomes more complicated. The particle-particle contact now occurs in a plane. The tangential component of the relative velocity is always in this plane and vertical to the normal unit vector according to the definition. Since the normal unit vector is not necessarily situated in the same plane at any time, it is desirable to transfer the old tangential displacement to the new contact plane before we calculate the new tangential displacement. To this end, a 3D rotation of the old tangential displacement should be applied. As... 

Fig. 13. The rotation of the contact plane during particle-particle collisions.

The analysis of such patterns reveals that the microcrystals are preferentially oriented with their (021) planes, the contact planes, parallel to the substrate s surface. The interesting point is that, in order to satisfy such orientation, the hydrogen bonds of the dimers at the interface have to be broken and in addition some reorganization of the molecules is needed (see Fig. 5.6(g)). In conclusion, the molecule-substrate interactions are sufficiently strong (larger yuns and y nv values) to induce COO Aik bonds, where Aik represents sodium and potassium, but the growing crystals adapt their structure in order to crystallize in the known monoclinic bulk phase. 

To show that shear, due to a discontinuous rate of straining, is at a maximum at the upper and lower (contact) planes of an explosive sample, impacted in Kholevo No 2, and zero at its mid-plane, A B performed the following experiment. Two sets of 1mm thick HMX samples were prepared set 1 contained... 

The incipient gas velocity for a particle rolling along the wall can be determined by the torques exerted on the particle. Assuming that the drag force, gravitational force, and lift force are exerted through the central point of the sphere, the balance of the torques about the uppermost point of the particle-wall contact plane (see Fig. 11.8) can be given by... 

Both Form I (considered later) and Form II can be obtained by epitaxial crystallization. At atmospheric pressure, the unstable, chiral Form II can be forced to crystallize by using an appropriate substrate, namely 2-quinoxalinol, as assessed by the electron diffraction pattern (Fig. 5a) (no AFM images are available) [32], The contact plane is found to be (110)F... 

Fig. 5 (a) Diffraction pattern of sPP crystallized in its chiral Form II on p-quinoxalinol. The presence of reflections characteristic of this form and not observed for Form I confirms that the thin film as a whole is mostly in Form II. Chain axis vertical, (110) contact plane. Reproduced from [32] with permission (b) Illustration of the topographic interactions that induce Form II rather than Form I the hilly surface of the 2-quinoxalinol substrate (left, seen parallel to the contact face) can only accommodate the Form II (110) plane (middle, three chains shown, as seen parallel to the contact plane, chain axis vertical). The (110) plane of Form I (left, also three chains represented) has a profile that is not compatible with that of the substrate contact face... 

Fig. 10 Measured crack lengths, L, in an epoxy polymer as a function of the number of cycles and the imposed lateral displacement. The crack length was measured in the contact plane from in situ observations. Amplitude of the relative displacement Black circles 15 xm, white circles 20 pm, white squares 25 pm, black squares 30 pm, white diamonds 60 pm. Dotted lines indicate the occurrence of britde failure events during the course of the contact fatigue experiments...

Fig. 12 Theoretical analysis of initial crack growth directions. In a first step, the three-dimensional elastic contact stress field is calculated within the polymer body under small amplitude reciprocating micro-motions. A two-dimensional analysis of crack initiation is subsequently carried out using the calculated stress values in the meridian plane of the contact (Oxz). Average shear (rm) and tensile (crm) stresses are calculated for different locations in the contact and for different orientations, a, with respect to the normal to the contact plane...

This combined analysis of AoA and Ar, therefore establishes that the main cracks that nucleate close to the contact edge correspond to predominantly tensile fatigue cracks. This conclusion remains valid whatever the contact condition (partial slip or gross slip). In addition, the distribution of within the contact plane is of interest (Fig. 15). The maximum amplitude... 

Interestingly, the ductile-brittle transition observed for the MIM system provided an opportunity to assess the material fracture toughness, which was not possible using classical fracture mechanics tests due to the intrinsic brittleness of the MIM system. The measurement of the critical crack length, Lc, in the contact plane at the onset of brittle propagation allows estimation of a fracture toughness K C = a x+JnLc in the order of 0.85 MPa m1/2, i.e. much less than that of a poly(methylmethacrylate) homopolymer (1.20 MPa m1/2). 

Fig. 4 Theoretical modelling of crack initiation. Calculation of the average shear (Xm) and tensile (ctm) stresses as a function of crack orientation, a, with respect to the contact plane.

Fig.7 Distribution of the maximum amplitude of the tensile stress, Act i, in the contact plane (z = 0). The dotted circle delimits the contour of the contact area.

A much more general mechanism for this kind of application is schematically represented in Fig. 3(b). A third phase (3) is inserted as an active material between the contact plane (1), made of metal or any inert metal-free material such as glassy carbon or carbon-black-filled polymers with a good electronic conductivity, and the... 

The effect of single and multiple isotropic layers or coatings on the end of a circular flux tube has been determined by Antonetti [2] and Sridhar et al. [107]. The heat enters the end of the circular flux tube of radius b and thermal conductivity k3 through a coaxial, circular contact area that is in perfect thermal contact with an isotropic layer of thermal conductivity k, and thickness This layer is in perfect contact with a second layer of thermal conductivity k2 and thickness t2 that is in perfect contact with the flux tube having thermal conductivity k3 (Fig. 3.22). The lateral boundary of the flux tube is adiabatic and the contact plane outside the contact area is also adiabatic. The boundary condition over the contact area may be (1) isoflux or (2) isothermal. The dimensionless constriction resistance p2 layers = 4k3aRc is defined with respect to the thermal conductivity of the flux... 

The Cartesian co-ordinate system shown in Figure 22 is used to orientate and locate the measuring devices. The origin is located at the intersection of the tunnel axis and the contact plane between the concrete plug and the bentonite buffer. Positive X axis is directed along the tunnel axis towards the other end of the test section. The Z-axis is vertical, pointing upwards and the Y-axis is perpendicular to the (XZ) plane in the position indicated in Figure 22. 

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